Not sure if you have thought about it or not, but since you are planning on keeping the cpu and already have 8gb of decent ddr2, why not just upgrade PSU and video card?

You could definetly get a whole computer for under $1000, but since you are still satified with your CPU it would be a much cheaper option that would massively improve gaming performance. The upgrade from ddr2 to ddr3 would help performance, but but its not going to be night and day. Also, if you ended up not satisfied with the upgrade you could just carry these new parts forward into whatever you decide to buy.

If I was in your shoes I would go with a quality psu (seasonic, antec, xfx, corsair,etc that is 600w or greater) and a gtx 560ti or hd 6950. Not sure what resolution you are gaming at, but either of these will handle your needs. (if you are at lower resolutions then a cheaper video card would suffice...ex gtx 460 768mb/1gb not the SE, or hd 6850/6870 ). If you decide to make the leap to a new motherboard, ram, and cpu then I would have to recommend you switch to intel or wait for bulldozer if you want to stay AMD.

EDIT: your cpu, phenom II x4 920, was one of the original phenom II processors. It is an AM2+ chip and not AM3, which means you can only use it in am2+ boards and only with ddr2. This pretty much reinforces my previous thoughts.